Ultraviolet dissipation and defect OPE in bottom-up holographic interfaces

Abstract

We study the radial ultraviolet dissipation quantity $c_{UV}$ defined in arXiv:2601.16888v3 and defect OPE data in bottom-up holographic interfaces. We relate $c_{UV}$ along with the defect primary spectrum and BOPE coefficients in the large defect dimension limit to the optical length $\rho$ in the holographic bulk. In addition, we prove a new holographic bound for conformal interfaces relating entanglement entropy, energy transmission and UV dissipation: \[ c_{LR}\geq \frac{2c_{\mathrm{eff}}}{2+π(c/c_{\mathrm{UV}}-1)}. \] This compliments the upper bound of $c_{LR}$ by $c_{\text{eff}}$ proved in arXiv:2404.01515.